Fungsi Distribusi Peluang

  • Pencipta
    Topik Pertanyaan
  • #13385
    Ryennn n
    Peserta

    Misalnya fungsi distribusi dari x berbentuk
    F(x)=0; x < -1
    =(1/4)(x+2); -1 ≤ x < 1
    = 1; 1 ≤ x.
    Hitunglah P(-0,5 < x ≤ 0,5) dan P(X = 0)

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  • Penulis
    Jawaban
  • #13398
    StatistikaA
    Peserta

    \[\begin{aligned}F(x)&=0 ; x < -1 \\F(x) &= \frac{1}{4} (x+2) ; -1 \leq x< 1\\F(x) &= 1 ; 1\leq x\end{aligned}\]
    Hitung \(P(-0,5 < x ≤ 0,5)\)dan \(P(X = 0) \)
    \[\begin{aligned}P(-0,5 <x< 0,5) &= F(0,5) – F(-0,5)\\&= \left((\frac{1}{4})(0,5+2)\right)-\left((\frac{1}{4})(-0,5+2)\right)\\&=\frac{1}{4}.\frac{5}{2}-\frac{1}{4}.\frac{3}{2}\\&=\frac{5}{8}-\frac{3}{8}\\&=\frac{2}{8}\end{aligned}\]
    \[\begin{aligned}P(x=0) &= F(0)\\&=\frac{1}{4}(0+2)\\&=\frac{1}{2}\end{aligned}\]

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